Ab initio derivation of the crystal field parameters for lanthanide ions: The f1 case

The crystal field theory as explained by Abragam and Bleaney in their landmark 1970 book on transition-ion electron paramagnetic resonance remains a cornerstone in the development of luminescence applications and molecular magnets based on the f-elements. The modern numerical derivation of the 27 Bkq Stevens crystal field parameters (CFPs), which describe the splitting of the energy levels of a central ion, is traditionally achieved through the effective Hamiltonian theory and multiconfiguration wave function theory calculations, insofar as the lowest J level fully captures the targeted low-energy physics. In this study, we present a novel theoretical approach for determining the CFPs. The procedure resembles the traditional extraction path but crucially accounts for the full |J, MJ⟩ space of an ion configuration with L = 3 and S = 1/2. By demonstrating the extraction procedure using the simplest case of a CeIII 4f1 ion with a crystal-field split J ∈ 5/2, 7/2 manifold, it is shown for the first time that a unique set of CFPs describes the splitting and mixing of both the J manifolds. In fact, this J/J' mixing is analogous to the "spin mixing" in binuclear transition metal complexes. At the employed level of calculation, we demonstrate that there is no spin-orbit coupling influence on the CFP values. Moreover, for the 4f1 case, the present extraction yields crystal-field and spin-orbit parameters similar to those obtained from ab initio ligand field theory. This study represents the first step of a larger effort in reviewing the theory and extraction procedures of CFPs in f-element complexes.